Hamming Path

The Hamming distance between two binary codes of the same length is the number of positions where their bits differ.

You are given N distinct binary codes, and every code has length K. The codes are numbered from 1 to N in the order they are given.

A Hamming path is a sequence of code numbers where each neighboring pair in the sequence has Hamming distance exactly 1.

Given two different code numbers A and B, find a shortest Hamming path from A to B.

The first line contains two integers N and K (3 <= N <= 1,000, 2 <= K <= 30).

Each of the next N lines contains one binary code of length K, with no spaces. All codes are distinct and are numbered from 1 to N in input order.

The last line contains two different code numbers A and B.

If a Hamming path exists between the two given codes, print the code numbers on any shortest such path from A to B, separated by single spaces.

If there is more than one shortest path, print any one of them. If no path exists, print -1.